IMAGE RECONSTRUCTION FROM LIMITED PROJECTIONS USING THE ANGULAR PERIODICITY OF THE FOURIER TRANSFORM OF THE RADON TRANSFORMS OF AN OBJECT.

M. Soumekh

doi:10.1007/978-1-4613-2779-0_4

IMAGE RECONSTRUCTION FROM LIMITED PROJECTIONS USING THE ANGULAR PERIODICITY OF THE FOURIER TRANSFORM OF THE RADON TRANSFORMS OF AN OBJECT.

M. Soumekh

Department of Electrical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

A noniterative method of image reconstruction from limited projections is presented. The approach is based on the periodicity property of the Fourier transform of the Radon transforms of an object (observed function) with respect to the projection angle. This functional characteristic of the observed function is utilized to interpolate the missing line integrals by a truncated Fourier series expansion. Methods for finding the components of the truncated Fourier series from the available data are given. Use of a priori information in formulating the solution of the truncated Fourier series is also discussed.

Original language	English
Title of host publication	Acoustical Imaging
Subtitle of host publication	Proceedings of the International Symposium
Publisher	Plenum Press
Pages	31-42
Number of pages	12
ISBN (Print)	0306417170, 9780306417177
DOIs	https://doi.org/10.1007/978-1-4613-2779-0_4
State	Published - 1984

Publication series

Name	Acoustical Imaging: Proceedings of the International Symposium
Volume	13
ISSN (Print)	0270-5117

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10.1007/978-1-4613-2779-0_4

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Soumekh, M. (1984). IMAGE RECONSTRUCTION FROM LIMITED PROJECTIONS USING THE ANGULAR PERIODICITY OF THE FOURIER TRANSFORM OF THE RADON TRANSFORMS OF AN OBJECT. In Acoustical Imaging: Proceedings of the International Symposium (pp. 31-42). (Acoustical Imaging: Proceedings of the International Symposium; Vol. 13). Plenum Press. https://doi.org/10.1007/978-1-4613-2779-0_4

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title = "IMAGE RECONSTRUCTION FROM LIMITED PROJECTIONS USING THE ANGULAR PERIODICITY OF THE FOURIER TRANSFORM OF THE RADON TRANSFORMS OF AN OBJECT.",

abstract = "A noniterative method of image reconstruction from limited projections is presented. The approach is based on the periodicity property of the Fourier transform of the Radon transforms of an object (observed function) with respect to the projection angle. This functional characteristic of the observed function is utilized to interpolate the missing line integrals by a truncated Fourier series expansion. Methods for finding the components of the truncated Fourier series from the available data are given. Use of a priori information in formulating the solution of the truncated Fourier series is also discussed.",

author = "M. Soumekh",

year = "1984",

doi = "10.1007/978-1-4613-2779-0\_4",

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series = "Acoustical Imaging: Proceedings of the International Symposium",

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IMAGE RECONSTRUCTION FROM LIMITED PROJECTIONS USING THE ANGULAR PERIODICITY OF THE FOURIER TRANSFORM OF THE RADON TRANSFORMS OF AN OBJECT. / Soumekh, M.
Acoustical Imaging: Proceedings of the International Symposium. Plenum Press, 1984. p. 31-42 (Acoustical Imaging: Proceedings of the International Symposium; Vol. 13).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - A noniterative method of image reconstruction from limited projections is presented. The approach is based on the periodicity property of the Fourier transform of the Radon transforms of an object (observed function) with respect to the projection angle. This functional characteristic of the observed function is utilized to interpolate the missing line integrals by a truncated Fourier series expansion. Methods for finding the components of the truncated Fourier series from the available data are given. Use of a priori information in formulating the solution of the truncated Fourier series is also discussed.

AB - A noniterative method of image reconstruction from limited projections is presented. The approach is based on the periodicity property of the Fourier transform of the Radon transforms of an object (observed function) with respect to the projection angle. This functional characteristic of the observed function is utilized to interpolate the missing line integrals by a truncated Fourier series expansion. Methods for finding the components of the truncated Fourier series from the available data are given. Use of a priori information in formulating the solution of the truncated Fourier series is also discussed.

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DO - 10.1007/978-1-4613-2779-0_4

M3 - Conference contribution

AN - SCOPUS:0021616877

SN - 0306417170

SN - 9780306417177

T3 - Acoustical Imaging: Proceedings of the International Symposium

SP - 31

EP - 42

BT - Acoustical Imaging

PB - Plenum Press

ER -

IMAGE RECONSTRUCTION FROM LIMITED PROJECTIONS USING THE ANGULAR PERIODICITY OF THE FOURIER TRANSFORM OF THE RADON TRANSFORMS OF AN OBJECT.

Abstract

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